Abstract
The study's primary purpose is to investigate the $\mathscr{A}/\mathscr{T}$ structure of a quotient ring, where $\mathscr{A}$ is an arbitrary ring and $\mathscr{T}$ is a semi-prime ideal of $\mathscr{A}$. In more details, we look at the differential identities in a semi-prime ideal of an arbitrary ring using $\mathscr{T}$-commuting generalized derivation. The article proves a number of statements. A characteristic representative of these assertions is, for example, the following Theorem 3: Let $\mathscr{A}$ be a ring with $\mathscr{T}$ a semi-prime ideal and $\mathscr{I}$ an ideal of $\mathscr{A}.$ If $(\lambda, \psi)$ is a non-zero generalized derivation of $\mathscr{A}$ and the derivation satisfies any one of the conditions:\1)\ $\lambda([a, b])\pm[a, \psi(b)]\in \mathscr{T}$,\ 2) $\lambda(a\circ b)\pm a\circ \psi(b)\in \mathscr{T}$,$\forall$ $a, b\in \mathscr{I},$ then $\psi$ is $\mathscr{T}$-commuting on $\mathscr{I}.$
Furthermore, examples are provided to demonstrate that the constraints placed on the hypothesis of the various theorems were not unnecessary.
Publisher
Ivan Franko National University of Lviv
Reference20 articles.
1. F.A.A. Almahdi, A. Mamouni, M. Tamekkante, A generalization of Posner’s theorem on derivations in rings, Indian J. Pure Appl. Math., 51 (2020), №1, 187–194.
2. M. Ashraf, A. Ali, S. Ali, Some commtativity theorems for rings with generalized derivations, Southeast Asian Bull. Math., 31 (2007), 415–421.
3. M. Ashraf, N. Rehman, On commutativity of rings with dervations, Results Math., 42 (2002), №1–2,3–8.
4. H.E. Bell, W.S. Martindale III, Centralizing mappings of semiprime rings, Canad. Math. Bull., 30 (1987), №1, 92–101.
5. M. Hongan, A note on semiprime rings with derivations, Internat. J. Math. Math. Sci., 20 (1997), №2, 413–415.
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4 articles.
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